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anonymous

  • 5 years ago

9x^2(2x+7)-12x(2x+7)=3x(2x+7)(3x-4) ...at the end where did the (3x-4) come from?

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  1. amistre64
    • 5 years ago
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    As far as I can tell; you typed it in there. :)

  2. anonymous
    • 5 years ago
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    It's on the website where I found this openstudy group. I never answered it. It says that's the answer and I'm a bit confused.

  3. amistre64
    • 5 years ago
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    You have 2 numbers that are the same (2x+7) and (2x+7); so factor those out and your left with: (2x+7) (9x^2-12x) does this make sense? Now, we can factor (9x^2 -12x) even further to get: 3x (x-4) ; it should be: (3x) (2x+7) (x-4). It would be a typo :)

  4. amistre64
    • 5 years ago
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    ack!! my mistake 3x(3x-4) is correct... do you know why?

  5. anonymous
    • 5 years ago
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    No, I don't know why. xD I have a math 11 test tomorrow and I'm a bit nervous. I can't get the hang of this stuff. :/ Mind explaining?

  6. amistre64
    • 5 years ago
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    do you understand the first step....how to factor out (2x+7) and get left with (9x^2 -12x)? It is the opposite of distirbuting...

  7. anonymous
    • 5 years ago
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    The question is 9x^2(2x+7)-12x(2x+7) and I know that theres a 3x in each term and a (2x+7) so you can factor those out right? So on the site it says it equals 3x(2x+7)(3x-4) and I understand how I got the 3x(2x+7) because both terms have it, but I'm so lost as to where the 3x-4 came up.

  8. amistre64
    • 5 years ago
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    lets take it step by step and you will see where it comes from...fair enough?

  9. anonymous
    • 5 years ago
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    Kay. :)

  10. amistre64
    • 5 years ago
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    9x^2(2x+7)-12x(2x+7) has a common factor that is blaringly obvious. It is (2x+7) right? just let me know if this is correct....

  11. anonymous
    • 5 years ago
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    Yes, but doesn't it have 3x as well?

  12. amistre64
    • 5 years ago
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    3x doesnt matter yet; it will come, but not yet. lets clean it up some first ok?

  13. anonymous
    • 5 years ago
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    kk, so yes, 2x+7

  14. amistre64
    • 5 years ago
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    when we factor out (2x+7) are we left with: (2x+7) (9x^2 -12x) ? yes or no...

  15. amistre64
    • 5 years ago
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    think of (2x+7) call it A if you have to..

  16. anonymous
    • 5 years ago
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    yes, we're left with it.

  17. anonymous
    • 5 years ago
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    sorry i'm talkign long to reply. keep pressing enter instead of post.

  18. anonymous
    • 5 years ago
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    taking.*

  19. amistre64
    • 5 years ago
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    its ok... Now we can factor (9x^2 -12x). Do you see how we could do that?

  20. anonymous
    • 5 years ago
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    Oh wait! So, you can take out a 3 because of 9 and 12, and you can also take out an x, hence 3x, and you can get a 4 because 3X4 = 12.

  21. amistre64
    • 5 years ago
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    you are brilliant :)

  22. anonymous
    • 5 years ago
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    So 3x(3-4)

  23. anonymous
    • 5 years ago
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    So once we get that we just put the 2x+7 back in?

  24. anonymous
    • 5 years ago
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    And our 3x would go in front.

  25. amistre64
    • 5 years ago
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    3x(3x - 4) = 9x^2 -12x right?

  26. amistre64
    • 5 years ago
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    but yes, you can put the numbers back in whatever order you feel comfortable with.

  27. anonymous
    • 5 years ago
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    yes! :D

  28. anonymous
    • 5 years ago
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    So that's why there was a 4. I was confused about that but now I get it, because of the 3-4, 3x4= 12. Makes so much more sense now.

  29. amistre64
    • 5 years ago
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    Just remember to take things step-by-step and it should all work out :)

  30. anonymous
    • 5 years ago
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    I'm still bad at this stuff, though. I understand that question, but there's like 4 different types of facorting we're doing in class and I get confused when I'm doing problems because I'm not sure which one I'm supposed to use.

  31. amistre64
    • 5 years ago
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    I hate the way they teach factoring in school. Because there is only one method that you actually use.. it is to "un" distribute or take apart; what was already put together.

  32. anonymous
    • 5 years ago
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    & my math teacher picks favorites, if you're not up there in your math grades then he'll get mad. It's really annoying. I failed my past two math tests. I had 88 on my first test, but when he started teaching I dropped down to half that mark, to like 44. Tomorrow's test is kinda crucial.

  33. amistre64
    • 5 years ago
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    what factoring methods do you need help with?

  34. anonymous
    • 5 years ago
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    I'm strong in every other subject besides math. Anyways, care to help me with a couple more problems?

  35. anonymous
    • 5 years ago
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    I'll list a problem I was having trouble with today. One second, I'll find it in my book.

  36. anonymous
    • 5 years ago
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    x^2+8x+12 x^2+3x-18 and it's supposed to be over each other.

  37. anonymous
    • 5 years ago
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    The top part = (x+2)(x+3) right?

  38. amistre64
    • 5 years ago
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    glorified fractions is all that is. The equation gives you clues as to what to do. Do you see the "sign" of the last term?

  39. anonymous
    • 5 years ago
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    What sign? I'm not sure what you mean by that, sorry.

  40. amistre64
    • 5 years ago
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    (+12) OR (-18) the last term is gotten by multipying 2 numbers together. What combination of "signs" when multiplied give you a (+) answer? What combination of "signs" when multiplied give you a (-) answer? Can you tell me?

  41. anonymous
    • 5 years ago
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    two positives = positive, two negatives = positive, and a - and a + = a -, right?

  42. amistre64
    • 5 years ago
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    thats right. So the last term gives us a clue about our middle term. Becuase the middle term takes those same 2 numbers and adds them together. Lets focus on the top: +8 +12. we need 2 numbers that are either (-)(-) or (+)(+) to get the (+12) right? and they need to add together to get a (+) for the middle term (+8). Does this make sense?

  43. anonymous
    • 5 years ago
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    Yeah that makes sense, we're trying to get a LCD?

  44. anonymous
    • 5 years ago
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    2 and 6?

  45. amistre64
    • 5 years ago
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    we will soon enough; but lets take it step by step. We can start to set up our answer like this: Good now... (x 2 ) (x 6 ) what "sign" do we need to use to fill this in? to get a (+12) and a (+8)

  46. anonymous
    • 5 years ago
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    +

  47. amistre64
    • 5 years ago
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    Yes, (x+2) (x+8) is the answer for the top; store it away somewhere where it wont get broken...

  48. amistre64
    • 5 years ago
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    opps... make that (x+2)(x+6) and feel free to correct me :)

  49. anonymous
    • 5 years ago
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    That's the answer for the top? Don't the 6 break down to a 3? Or we can't do that because we're only going half of 12?

  50. amistre64
    • 5 years ago
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    there is nothing that x and 6 have in common so it is as far as it will go. to double check, multiply them back together.

  51. anonymous
    • 5 years ago
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    I understand.

  52. amistre64
    • 5 years ago
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    x^2 +3x -18 the last term tells us what signs we need to use. and the middle term tells us which of those signs gets the bigger number. Does that make sense?

  53. amistre64
    • 5 years ago
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    what makes a (-) when multiplied together?

  54. anonymous
    • 5 years ago
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    + and -

  55. anonymous
    • 5 years ago
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    I don't know what you mean by which sign gets the bigger number, though.

  56. amistre64
    • 5 years ago
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    good; then its our only option: (x+ )(x- ) is what we are dealt. now find 2 numbers that multiply to 18 and "subtract" to get 3. Do you see why we need the (+)number to be bigger than the (-)number to get (+3)?

  57. anonymous
    • 5 years ago
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    I'm a bit confused.

  58. amistre64
    • 5 years ago
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    the numbers are gonna be 6 and 3... to equal 18 right? -6 +3 = -3 +6 -3 = +3 do you see it?

  59. anonymous
    • 5 years ago
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    I thought we were trying to equal 18? Not - and +3?

  60. anonymous
    • 5 years ago
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    -3*

  61. amistre64
    • 5 years ago
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    ok...we can do that as well; what are the factors of 18 that subtract to get (+3) for a middle term? 1 and 18 2 and 9 3 and 6 thats it... right?

  62. anonymous
    • 5 years ago
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    yep

  63. amistre64
    • 5 years ago
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    one number has to be (-) and the other number has to (+) In order to get the (+3) for the middle term, the largest number has to be (+) such as: +6 -3 = +3 and +6 times -3 equals -18 does this make sense?

  64. anonymous
    • 5 years ago
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    yes, it does!

  65. amistre64
    • 5 years ago
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    then we can fill in our stuff now: (x +6) (x -3) is our answer. for the bottom. Can we cross anything out from top to bottom that are alike?

  66. anonymous
    • 5 years ago
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    x+6

  67. amistre64
    • 5 years ago
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    Good, and we are left with: (x+2)(x+6) (x+2) ---------- = ----- (x+6)(x-3) (x-3)

  68. anonymous
    • 5 years ago
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    so then it's gonna be x+2 over x+3

  69. anonymous
    • 5 years ago
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    haha yep!

  70. anonymous
    • 5 years ago
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    wait, -3

  71. anonymous
    • 5 years ago
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    thats what I had written down on paper, typo on here. lol.

  72. amistre64
    • 5 years ago
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    i wish I had time for more, but my macroeconomics class is starting and running for the next 2 hours. You can do this, it is really stuff you already know :)

  73. anonymous
    • 5 years ago
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    Thanks for your help, and perfect timing. I have to go right now too.

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